What is reason of Buddhism mostly spread on hilltops of India then in plains of India? Moreover Dalai Lama lives on Hilltop; as he can live in plains. Is there any reason of choosing mountains for residence?
The Buddha mostly lived and taught in the Gangetic plains of India, and there's no record of him sojourning to the Himalayas like most Indian mystics.
However he is also said to have favored the Vulture peak near the city of Rajgir, so it's not like he exclusively preferred the plains either.
Most mystics like mountains for the solitude, in the Buddha's times it was possible to find it in the tropical Indian forests as well. In modern times, forest monks in Indochina keep the forest tradition alive.
The Buddha often chose meditative spots for the calm and tranquility, where meditation could proceed undisturbed, however he was also aware of spirits and other hinderances that could arise and rejected some otherwise calm places to meditate.
Wikipedia's description of the Vinaya says,
It is thought that originally there were no rules and the Buddha and his disciples just lived in harmony when they were together. Most of the time they would have been wandering alone, but every year, during the monsoon season when travelling became impossible, the bhikkhus would come together for a few months. As the sangha became bigger and started accepting people of lesser ability who remained unenlightened, it became necessary to begin having rules.
I don't know why Dharamsala was chosen. It's on the edge of the Himalayas: maybe "close to the Himalayas" is why it's hilly and was suitable for Tibetans-in-exile.